Problem: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}9x+4y &= 1 \\ 6x+y &= 1\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $y = {-6x+1}$ Substitute this expression for $y$ in the first equation. $9x+4({-6x + 1}) = 1$ $9x - 24x + 4 = 1$ Simplify by combining terms, then solve for $x$ $-15x + 4 = 1$ $-15x = -3$ $x = \dfrac{1}{5}$ Substitute $\dfrac{1}{5}$ for $x$ back into the top equation. $9( \dfrac{1}{5})+4y = 1$ $\dfrac{9}{5}+4y = 1$ $4y = -\dfrac{4}{5}$ $y = -\dfrac{1}{5}$ The solution is $\enspace x = \dfrac{1}{5}, \enspace y = -\dfrac{1}{5}$.